Which of the following numbers is a factor of 140? ${3,7,9,11,13}$
By definition, a factor of a number will divide evenly into that number. We can start by dividing $140$ by each of our answer choices. $140 \div 3 = 46\text{ R }2$ $140 \div 7 = 20$ $140 \div 9 = 15\text{ R }5$ $140 \div 11 = 12\text{ R }8$ $140 \div 13 = 10\text{ R }10$ The only answer choice that divides into $140$ with no remainder is $7$ $ 20$ $7$ $140$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $140$ $140 = 2\times2\times5\times7 7 = 7$ Therefore the only factor of $140$ out of our choices is $7$. We can say that $140$ is divisible by $7$.